Robustness of Emergent Schrödinger Symmetry in Spherically Symmetric Static Spacetimes with Matter Fields
Abstract: Recent pioneering works have revealed a hidden Schrödinger symmetry governing the mechanics of Schwarzschild-(A)dS black holes and cosmological models. This has opened an exciting path to describing quantum black holes and early universe dynamics in terms of quantum fluids, potentially governed by Gross-Pitaevskii-like equations. Inspired by these foundational results, this talk explores the robustness of such emergent Schrödinger symmetries when matter fields are explicitly coupled to spherically-symmetric static mini-superspaces.
First, we consider the inclusion of an electromagnetic field alongside a cosmological constant. We demonstrate that, by employing the exact same lapse choice identified in the previous vacuum (A)dS studies, the system naturally extends to exhibit a 3D Schrödinger symmetry.
Second, we investigate a system coupled to a massless scalar field. We show that the Schrödinger symmetry still remarkably emerges, but it is realized under a different choice of the lapse function. Interestingly, this specific lapse choice corresponds to using the massless scalar field as a relational time variable, offering a highly intriguing physical perspective. Furthermore, taking the vacuum limit under this new lapse choice also yields a 2D Schrödinger symmetry, complementing the existing framework.
Ultimately, our findings highlight the robustness of Schrödinger symmetry in gravitational mini-superspaces, further strengthening the anticipated mapping between black hole dynamics and quantum fluid models.